Encouraging people to eat healthy fats such as those found in olive oil or fish could help prevent more than a million deaths from heart disease worldwide each year, according to a new study.

In fact, the number of deaths from heart disease due to insufficient intake of healthy fats is almost three times' greater than the number of deaths due to excessive intake of saturated fats, according to the researchers. (Saturated fats are found in meat, cheeses, other dairy products as well as palm and coconut oils.)

"Policies for decades have focused on saturated fats as the priority for preventing heart disease, but we found that in most countries, a too-little intake of healthy fats was the big problem, bigger than saturated fat," said study author Dr. Dariush Mozaffarian, of the Friedman School of Nutrition Science and Policy at Tufts University in Boston.

In the study, researchers looked at data on people's diets and rates of death from heart disease from 186 countries in 2010. They estimated that 711,800 deaths from heart disease that year —or 10.3 percent of all deaths from heart disease worldwide — were due to people eating too little of the healthy fats called "omega-6 polyunsaturated fats," which can be found in vegetable oils.

In comparison, only about one-third of this number — 250,900 deaths, or 3.6 percent, of worldwide deaths from heart disease — were due to people eating too much saturated fat. [10 Amazing Facts About Your Heart]

The reason why so many more deaths could be prevented by increasing the intake of healthy fat is likely that there are additional health benefits when people consume omega-6 polyunsaturated fats instead of carbohydrates, the researchers said.

For example, "Instead of having two pieces of bread, have half a piece of bread and lots of olive oil or lots of healthy cooking oil or nuts," Mozaffarian told Live Science.

The researchers also found that 537,200 deaths in 2010 were due to an excessive intake of trans fat, including those in processed, baked and fried foods as well as cooking fats used in certain countries.

When the researchers looked at patterns of deaths from heart disease over time, they found that the proportion of deaths from heart disease due to an insufficient intake of omega-6 polyunsaturated fat declined 9 percent between 1990 and 2010.

In comparison, the proportion of deaths from heart disease due to a high intake of saturated fats declined by 21 percent. Deaths from heart disease due to a high consumption of trans fat rose by 4 percent during this time, the study found.

The new results suggest that "people should be increasing their healthy fats as long as they are doing it in place of animal fats, or, even better, in place of refined starch and carbohydrates," Mozaffarian said. Such healthy fats can be found in fish, nuts and vegetable oil, he said.

In the U.S., heart disease is the leading cause of death, and kills about 610,000 people every year, according to the Centers for Disease Control and Prevention. Along with eating a healthy diet, people can prevent heart disease by getting regular exercise, maintaining a healthy body weight and refraining from smoking.

The new study was published today (Jan. 20) in the Journal of the American Heart Association.